mne.minimum_norm.estimate_snr¶

mne.minimum_norm.estimate_snr(evoked, inv, verbose=None)[source]¶

Estimate the SNR as a function of time for evoked data.

Parameters:	evoked : instance of Evoked Evoked instance. inv : instance of InverseOperator The inverse operator. verbose : bool, str, int, or None If not None, override default verbose level (see mne.verbose()).
Returns:	snr : ndarray, shape (n_times,) The SNR estimated from the whitened data. snr_est : ndarray, shape (n_times,) The SNR estimated using the mismatch between the unregularized solution and the regularized solution.

Notes

snr_est is estimated by using different amounts of inverse regularization and checking the mismatch between predicted and measured whitened data.

In more detail, given our whitened inverse obtained from SVD:

$$\begin{split}\\tilde{M} = R^\\frac{1}{2}V\\Gamma U^T\end{split}$$

The values in the diagonal matrix $\\Gamma$ are expressed in terms of the chosen regularization $\\lambda\\approx\\frac{1}{\\rm{SNR}^2}$ and singular values $\\lambda_k$ as:

$$\begin{split}\\gamma_k = \\frac{1}{\\lambda_k}\\frac{\\lambda_k^2}{\\lambda_k^2 + \\lambda^2}\end{split}$$

We also know that our predicted data is given by:

$$\begin{split}\\hat{x}(t) = G\\hat{j}(t)=C^\\frac{1}{2}U\\Pi w(t)\end{split}$$

And thus our predicted whitened data is just:

$$\begin{split}\\hat{w}(t) = U\\Pi w(t)\end{split}$$

Where $\\Pi$ is diagonal with entries entries:

$$\begin{split}\\lambda_k\\gamma_k = \\frac{\\lambda_k^2}{\\lambda_k^2 + \\lambda^2}\end{split}$$

If we use no regularization, note that $\\Pi$ is just the identity matrix. Here we test the squared magnitude of the difference between unregularized solution and regularized solutions, choosing the biggest regularization that achieves a $\\chi^2$-test significance of 0.001.

New in version 0.9.0.